The known theory for a discrete oid shows that how to find a subset ∞ of which is a compact right topological semigroup (see section 2 for details).In this paper we try to find an analogue of almost periodic functions for oids. We discover, new compact semigroups by using a certain subspace of functions ∞ ( ) of ( ) for an oid for which is continuous on ∞ × ( ∪ ∞ ∪ ∞ ),where( ∪ ∞ ∪ ∞ ) is a suitable subspace of for a wide range.Mathematical Society Classification:2010, 54D35.

This paper presents an important new technique for studying a particular compact semigroup, N∪{∞}, the one-point compactification of positive integers with usual addition, which is an important semigroup. Indeed, the semigroup N ∪ {∞} is constructed as the quotient semigroup of a particular compact right topological semigroup. In the study of such a semigroup, a major role is played by the substructures called standard oids. For instance, some of the already known results on the structure of N ∪ {∞} are obtained as immediate consequences.

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